They are not known to be invasive here in Minnesota, Reid, and are not as resilient. I've seen the occasional reseeding in yard situations, but have never seen them proliferate in the wild. When pruned, sometimes they do come back if we cut them to the ground here, but don't be surprised if the result is less than satisfactory. Really though, you've hardly anything to lose if you want to start small again; if it dies just plant another, or better yet, plant something more interesting, like Leatherwood, Hazel or a viburnum.
Minnesota ranks invasiveness of species:
A. ―Severe threat‖ - known to be in the state
B. ―Severe threat‖ - not known to be in the state
C. ―Moderate threat‖ - known to be in the state
D. ―Moderate threat‖ - not known to be in the state
E. ―Minimal‖ - known to be in the state
F. ―Minimal‖ - not known to be in the state
G. ―Watch / Unknown threat‖
H. Considered But Not Ranked
I. Severe pests in other areas, but could not establish in Minnesota.
While Burning bush (Euonymus alatus) is known to be invasive in many states in the eastern half of the US for many many years, for our state, Minnesota ranks it as "G".